Let’s just keep it simple: to get an artificial gravity of 0.5g, you will need a radius of 450 meters and a distance between the spacecraft and the counterweight of two times (900 meters).
Just for fun, the The Wikipedia page lists the distance of the tether at 450 meters. This would give a rotation radius of 225 meters. Using the same angular velocity, astronauts would have an artificial gravity of just 0.25g.
I mean, it’s not terrible. In fact, the gravitational field on Mars is 0.38g, so that would be almost enough for astronauts to prepare for work on Mars. But I’m going to stick with my artificial gravity of 0.5g and a tie-down length of 900 meters.
What would it be like to slide a tie off?
Without going into too much detail, let’s consider what would happen if an astronaut were to climb one of the spacecraft’s cables to the counterweight on the other side for some reason. Maybe life is just better on the other side – who knows?
When the astronaut starts the cable (I call the opposite direction to artificial gravity “up”), physics dictates that they feel the same apparent weight as the other astronauts on the spacecraft. However, as they climb higher on the cable, their circular radius (their distance from the center of rotation) decreases, which also decreases artificial gravity. They would continue to feel lighter until they reached the center of the tether, where they would feel weightless. As they continued their journey to the other side, their apparent weight began to increase – but in the opposite direction, pulling them toward the counterweight at the other end of the lanyard.
But it’s not very exciting for a movie. So here’s something very dramatic instead. Suppose an astronaut starts near the center of rotation with very little artificial gravity. Instead of slowly descending the lanyard, what if it just let the false gravity shoot she down? How fast would she go when she got to the end of the line? (It would be sort of like falling to Earth, except that when it “falls,” the gravitational force increases as its distance from the center increases. In other words, the farther it falls, the greater the force on it. big.)
Since the force exerted on the astronaut changes as he descends, this becomes a more difficult problem. But don’t worry, there is an easy way to get a solution. It might sound like a cheat, but it works. The key is to break the movement down into tiny chunks of time.
If we consider its movement during a time interval of only 0.01 seconds, then it is not moving very far. This means that the artificial force of gravity is mostly constant, since its circular radius is also approximately constant. However, if we assume a constant force during this short time interval, we can use simpler kinematic equations to find the position and speed of the astronaut after 0.01 seconds. Then we use his new position to find the new strength and start the whole process all over again. This method is called a numerical calculation.
If you want to model the movement after 1 second, you will need 100 of these 0.01 time intervals. You can do this calculation on paper, but it’s easier to do it with a computer program. I’ll take the easy way out and use Python. You can see my code here, but here’s what it would look like. (Note: I enlarged the size of the astronaut so you can see it, and this animation works at 10x speed.)
For this slide on the cable, it takes about 44 seconds for the astronaut to slide with a final speed (in the direction of the cable) of 44 meters per second, or 98 miles per hour. So this is do not a sure thing to do.